A global pb-2 Rayleigh-Ritz method is used to study the free vibration
behaviour of trapezoidal Mindlin plates with different combinations o
f boundary conditions. The Mindlin theory is used to account for the e
ffects of shear deformation and rotary inertia. The governing energy f
unctional for the plate is derived and minimized to arrive at the eige
nvalue equation. In the process, the shape functions are assumed in a
set of two-dimensional mathematically complete polynomials which satis
fy the geometric boundary conditions of the plate. This procedure has
been implemented numerically to compute the vibration frequencies for
trapezoidal Mindlin plates. Convergence and comparison studies have be
en carried out to verify the accuracy of this method. Sets of first kn
own results have been presented for trapezoidal Mindlin plates of vary
ing thickness, aspect ratio and boundary constraint. These new results
enhance the database of vibration solutions.